Paper Detail
Chenyu Zhu, Ruoyu Zhao, Zhichao Lu
Modern Transformer design and compression both reduce to allocating capacity under a budget. The standard scalars for these decisions, #Params and #FLOPs, capture size and compute but not architectural structure: two architectures with identical parameter budgets but different depth-width, head, or FFN allocations receive identical scores yet behave differently. We propose Neural Spectral Capacity (NSC), a closed-form scalar grounded in the singular-value spectrum of each weight matrix. Under standard random initialization, the Marchenko-Pastur law renders NSC computable from the architectural specification alone, with no model instantiation, data, or gradients. Its layer-wise additive structure admits NSC-DP, an exact dynamic-programming solver returning the architecture globally maximizing NSC under resource constraints in seconds on a CPU -- a guarantee that black-box search over existing training-free proxies cannot provide. Empirically, NSC outperforms #Params, #FLOPs, and representative training-free proxies in ranking across seven Transformer and CNN families (on FlexiBERT, τ= 0.505 on pairs differing in #Params by less than 10%, where #Params collapses to 0.082); NSC-DP discovers a Transformer-XL architecture on WikiText-103 that beats the human-designed baseline in 2 seconds; and prunes LLaMA-7B to the best 5.7B model across eight commonsense reasoning tasks without any calibration data, about 5900x faster than the strongest training-free proxy baseline.
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@misc{zhu2026neural,
title = {Neural Spectral Capacity: Measuring and Designing Architectures from Network Specification Alone},
author = {Chenyu Zhu and Ruoyu Zhao and Zhichao Lu},
year = {2026},
abstract = {Modern Transformer design and compression both reduce to allocating capacity under a budget. The standard scalars for these decisions, \#Params and \#FLOPs, capture size and compute but not architectural structure: two architectures with identical parameter budgets but different depth-width, head, or FFN allocations receive identical scores yet behave differently. We propose Neural Spectral Capacity (NSC), a closed-form scalar grounded in the singular-value spectrum of each weight matrix. Under st},
url = {https://huggingface.co/papers/2609.23087},
keywords = {code available, huggingface daily},
eprint = {2609.23087},
archiveprefix = {arXiv},
}
{}